• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.343-351
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• 2018

Brazilian disc test is one of the most widely used experiments in the literature of geo-mechanics. In this work, the pre-holed concrete Brazilian disc specimens are numerically modelled by a two-dimensional discrete element approach. The cracks initiations, propagations and coalescences in the numerically simulated Brazilian discs (each containing a single cylindrical hole and or multiple holes) are studied. The pre-holed Brazilian discs are numerically tested under Brazilian test conditions. The single-holed Brazilian discs with different ratios of the diameter of the holes to that of the disc radius are modelled first. The breakage load in the ring type disc specimens containing an internal hole with varying diameters is measured and the crack propagation mechanism around the wall of the ring is investigated. The crack propagation and coalescence mechanisms are also studied for the case of multi-holes' concrete Brazilian discs. The numerical and experimental results show that the breaking mechanism of the pre-holed disc specimens is mainly due to the initiation of the radially induced tensile cracks which are growth from the surface of the central hole. Radially cracks propagated toward the direction of diametrical loading. It has been observed that for the case of disc specimens with multiple holes under diametrical compressive loading, the breaking process of the modelled specimens may occur due to the simultaneous cracks propagation and cracks coalescence phenomena. These results also show that as the hole diameter and the number of the holes increases both the failure stress and the crack initiation stress decreases. The experimental results already exist in the literature are quit agree with the proposed numerical simulation results which validates this simulation procedure.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.569-582
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• 2018

Effects of crack separation, bridge area, on the tensile behaviour of concrete are studied experimentally and numerically through the Brazilian tensile test. The physical data obtained from the Brazilian tests are used to calibrate the two-dimensional particle flow code based on discrete element method (DEM). Then some specially designed Brazilian disc specimens containing two parallel cracks are used to perform the physical tests in the laboratory and numerically simulated to make the suitable numerical models to be tested. The experimental and numerical results of the Brazilian disc specimens are compared to conclude the validity and applicability of these models used in this research. Validation of the simulated models can be easily checked with the results of Brazilian tests performed on non-persistent cracked physical models. The Brazilian discs used in this work have a diameter of 54 mm and contain two parallel centred cracks ($90^{\circ}$ to the horizontal) loaded indirectly under the compressive line loading. The lengths of cracks are considered as; 10 mm, 20 mm, 30 mm and 40 mm, respectively. The visually observed failure process gained through numerical Brazilian tests are found to be very similar to those obtained through the experimental tests. The fracture patterns demonstrated by DEM simulations are mostly affected by the crack separation but the tensile strength of bridge area is related to the fracture pattern and failure mechanism of the testing samples. It has also been shown that when the crack lengths are less than 30 mm, the tensile cracks may initiate from the cracks tips and propagate parallel to loading direction till coalesce with the other cracks tips while when the cracks lengths are more than 30 mm, these tensile cracks may propagate through the intact concrete itself rather than that of the bridge area.

• Smart Structures and Systems
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• v.22 no.6
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• pp.675-687
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• 2018

In the previous studies on the porous rock strength the effect of pore number and its diameter is not explicitly defined. In this paper crack initiation, propagation and coalescence in Brazilian model disc containing a single cylindrical hole and or multiple holes have been studied numerically using PFC3D. In model with internal hole, the ratio of hole diameter to model diameter was varied between 0.03, 0.17, 0.25, 0.33, and 0.42. In model with multiple hole number of holes was different in various model, i.e., one hole, two holes, three holes, four holes, five holes, six holes, seven holes, eight holes and nine holes. Diameter of these holes was 5 mm, 10 mm and 12 mm. The pre-holed Brazilian discs are numerically tested under Brazilian test. The breakage load in the ring type disc specimens containing an internal hole with varying diameters is measured. The mechanism of cracks propagation in the wall of the ring type specimens is also studied. In the case of multi-hole Brazilian disc, the cracks propagation and b cracks coalescence are also investigated. The results shows that breaking of the pre-holed disc specimens is due to the propagation of radially induced tensile cracks initiated from the surface of the central hole and propagating toward the direction of diametrical loading. In the case of disc specimens with multiple holes, the cracks propagation and cracks coalescence may occur simultaneously in the breaking process of model under diametrical compressive loading. Finally the results shows that the failure stress and crack initiation stress decreases by increasing the hole diameter. Also, the failure stress decreases by increasing the number of hole which mobilized in failure. The results of these simulations were comprised with other experimental and numerical test results. It has been shown that the numerical and experimental results are in good agreement with each other.

• Geomechanics and Engineering
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• v.10 no.6
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• pp.775-791
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• 2016

The indirect tensile strengths (ITSs) of different cemented paste backfill mixes with different curing times were determined by considering crack initiation and fracture toughness concepts under different loading conditions of steel loading arcs with various contact angles, flat platens and the standard Brazilian test jaw. Because contact area of the ITS test discs developes rapidly and varies in accordance with the deformability, ITSs of curing materials were not found convenient to determine under the loading apparatus with indefinite contact angle. ITS values increasing with an increase in contact angle can be measured to be excessively high because of the high contact angles resulted from the deformable characteristics of the soft paste backfill materials. As a result of the change of deformation characteristics with the change of curing time, discs have different contact conditions causing an important disadvantage to reflect the strength change due to the curing reactions. In addition to the experimental study, finite element analyses were performed on several types of disc models under various loading conditions. As a result, a comparison between all loading conditions was made to determine the best ITSs of the cemented paste backfill materials. Both experimental and numerical analyses concluded that loading arcs with definite contact angles gives better results than those obtained with the other loading apparatus without a definite contact angle. Loading arcs with the contact angle of $15^{\circ}$ was found the most convenient loading apparatus for the typical cemented paste backfill materials, although it should be used carefully considering the failure cracks for a valid test.

• Computers and Concrete
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• v.20 no.1
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• pp.39-47
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• 2017

In this paper, mode I fracture toughness of rock was determined by direct and indirect methods using Particle Flow Code simulation. Direct methods are compaction tension (CT) test and hollow centre cracked quadratic sample (HCCQS). Indirect methods are notched Brazilian disk (NBD) specimen, the semi-circular bend (SCB) specimen, hollow centre cracked disc (HCCD), the single edge-notched round bar in bending (SENRBB) specimen and edge notched disk (END). It was determined that which one of indirect fracture toughness values is close to direct one. For this purpose, initially calibration of PFC was undertaken with respect to data obtained from Brazilian laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, the simulated models in five introduced indirect tests were cross checked with the results from direct tests. By using numerical testing, the failure process was visually observed. Discrete element simulations demonstrated that the macro fractures in models are caused by microscopic tensile breakages on large numbers of bonded discs. Mode I fracture toughness of rock in direct test was less than other tests results. Fracture toughness resulted from semi-circular bend specimen test was close to direct test results. Therefore semi-circular bend specimen can be a proper test for determination of Mode I fracture toughness of rock in absence of direct test.

• Computers and Concrete
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• v.18 no.1
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• pp.39-51
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• 2016

This paper considers the tensile strength of concrete samples in direct, CTT, modified tension, splitting and ring tests using both of the experimental tests and numerical simulation (particle flow code 2D). It determined that which one of indirect tensile strength is close to direct tensile strength. Initially calibration of PFC was undertaken with respect to the data obtained from Brazilian laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, validation of the simulated models in four introduced tests was also cross checked with the results from experimental tests. By using numerical testing, the failure process was visually observed and failure patterns were watched to be reasonable in accordance with experimental results. Discrete element simulations demonstrated that the macro fractures in models are caused by microscopic tensile breakages on large numbers of bonded discs. Tensile strength of concrete in direct test was less than other tests results. Tensile strength resulted from modified tension test was close to direct test results. So modified tension test can be a proper test for determination of tensile strength of concrete in absence of direct test. Other advantages shown by modified tension tests are: (1) sample preparation is easy and (2) the use of a simple conventional compression press controlled by displacement compared with complicate device in other tests.

• Smart Structures and Systems
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• v.22 no.4
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• pp.459-468
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• 2018

In this paper, the effect of non-persistent joints was determined on the behavior of concrete specimens subjected to biaxial loading through numerical modeling using particle flow code in two dimensions (PFC2D). Firstly, a numerical model was calibrated by uniaxial, Brazilian and triaxial experimental results to ensure the conformity of the simulated numerical model's response. Secondly, sixteen rectangular models with dimension of 100 mm by 100 mm were developed. Each model contains two non-persistent joints with lengths of 40 mm and 20 mm, respectively. The angularity of the larger joint changes from $30^{\circ}$ to $90^{\circ}$. In each configuration, the small joint angularity changes from $0^{\circ}$ to $90^{\circ}$ in $30^{\circ}$ increments. All of the models were under confining stress of 1 MPa. By using of the biaxial test configuration, the failure process was visually observed. Discrete element simulations demonstrated that macro shear fractures in models are because of microscopic tensile breakage of a large number of bonded discs. The failure pattern in Rock Bridge is mostly affected by joint overlapping whereas the biaxial strength is closely related to the failure pattern.

• Smart Structures and Systems
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• v.22 no.6
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• pp.663-673
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• 2018

In this study, the effect of particle size on the cracks propagation and coalescence or cracking pattern of the edge notched disc specimens are investigated. Firstly, calibration of PFC3D was performed using Brazilian experimental test output. Then micro parameters were used to build edge notched disc specimen. The horizontal wall of the assembly is let to move downward with a standard low speed of 0.016 m/s. The numerical results show that the tensile cracks are dominant failure pattern for the modeled discs. These tensile cracks initiate from the pre-existing notch tip and propagate parallel to the loading direction then interact with the upper boundary of the modeled specimen. As the size of the balls (ball diameter) decrease the number of tensile cracks increase. The tensile fracture toughness of the samples also decreases as the particle size increases. Understanding the crack propagation and crack coalescence phenomena in brittle materials such as concretes and rocks is of paramount importance in the stability analyses for engineering structures such as rock slopes, underground structures and tunneling.

• Computers and Concrete
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• v.32 no.5
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• pp.465-474
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• 2023

The point load test (PLT) is a widely-used alternative method in the field to determine the uniaxial compressive strength due to its simple testing machine and procedure. The point load test index can estimate the uniaxial compressive strength through conversion factors based on the rock types. However, the mechanism correlating these two parameters and the influence of the mechanical properties on PLT results are still not well understood. This study proposed a theoretical model to understand the mechanism of PLT serving as an alternative to the UCS test based on laboratory observation and literature survey. This model found that the point load test is a self-confined compression test. There is a compressive ellipsoid near the loading axis, whose dilation forms a tensile ring that provides confinement on this ellipsoid. The peak load of a point load test is linearly positive correlated to the tensile strength and negatively correlated to the Poisson ratio. The model was then verified using numerical and experimental approaches. In numerical verification, the PLT discs were simulated using flat-joint BPM of PFC3D to model the force distribution, crack propagation and BPM properties' effect with calibrated micro-parameters from laboratory UCS test and point load test of Berea sandstones. It further verified the mechanism experimentally by conducting a uniaxial compressive test, Brazilian test, and point load test on four different rocks. The findings from this study can explain the mechanism and improve the understanding of point load in determining uniaxial compressive strength.